Write the condition for unique solution of linear equation:

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\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

None

answer is B.

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Detailed Solution

Suppose there is system of equation such that,

\begin{matrix} a_{1} x + b_{1} y + c_{1} = 0 \\ a_{2} x + b_{2} y + c_{2} = 0 \end{matrix}

For the equation, condition for the unique solution is,

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

(for intersecting lines)
For the equation, condition for the infinite solution is,

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

(for coincident lines)
For the equation, condition for no solution is,

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

(for parallel lines)
Thus, condition for unique solution of linear equation

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

So, option 2 is correct.

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